Continuous Strong Markov Processes in Dimension One

1. Front Matter

   Pages I-XII

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2. Basic concepts and preparatory results

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 1-13

3. Classification of the points of the state space

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 15-25

4. Weakly additive functionals and time change of strong Markov processes

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 27-32

5. Semimartingale decomposition of continuous strong Markov semimartingales

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 33-52

6. Occupation time formula

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 53-77

7. Construction of continuous strong Markov processes

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 79-102

8. Continuous strong Markov semimartingales as solutions of stochastic differential equations

   • Sigurd Assing, Wolfgang M. Schmidt

   Pages 103-118

9. Back Matter

   Pages 119-138

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The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

• Markov process
• Martingale
• Semimartingale
• Stochastic calculus
• calculus

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